On the identifiability of dynamical networks * *Work supported by the Program Science Without Borders, CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnologico, Brazil, and by the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office.

Abstract

Abstract The identification of networks from measured data has been studied for many years in computer science and statistics. Central to this topic is the identifiability of the network, also called reconstructibility or faithfulness in these communities. This paper examines a class of networks in which the node signals, assumed measurable, are connected by linear time-invariant transfer functions, and in which a noise signal and/or a known excitation signal may or may not be present at each node. The paper discusses the notion of network identifiability. It then proposes a definition that is shown to be efficient for the reconstruction of a dynamical network from measured data. This allows us to exhibit a parametrization of all equivalent network models that are consistent with the data, and thereby to produce a range of sufficient conditions for network identifiability. These conditions (in the form of prior knowledge on the structure of the excitations) show that for the identification of a dynamical network a trade-off exists between excitation from known external signals and excitation from the noise.